Scientific Notation

Scientific Notation Video

 http://www.mathsisfun.com/numbers/scientific-notation.html

Scientific Notation (also called Standard Form in Britain) is a special way of writing numbers:

Like this:
Or this:

It makes it easy to use big and small values.

OK, How Does it Work?

Example: 700

Why is 700 written as 7 × 10² in Scientific Notation ?

700 = 7 × 100

and 100 = 10² (see powers of 10)

so 700 = 7 × 10²

Both 700 and 7 × 10² have the same value, just shown in different ways.

Example: 4,900,000,000

    1,000,000,000 = 10⁹ ,
so 4,900,000,000 = 4.9 × 10⁹ in Scientific Notation

The number is written in two parts:

• Just the digits (with the decimal point placed after the first digit), followed by
• × 10 to a power that puts the decimal point where it should be
  (i.e. it shows how many places to move the decimal point).

In this example, 5326.6 is written as 5.3266 × 10³,
because 5326.6 = 5.3266 × 1000 = 5.3266 × 10³

How to Do it

To figure out the power of 10, think "how many places do I move the decimal point?"

	If the number is 10 or greater, the decimal point has to move to the left, and the power of 10 will be positive.
	If the number is smaller than 1, the decimal point has to move to the right, so the power of 10 will be negative:

Example: 0.0055 would be written as 5.5 × 10^-3

Because 0.0055 = 5.5 × 0.001 = 5.5 × 10^-3

Example: 3.2 would be written as 3.2 × 10⁰

We didn't have to move the decimal point at all, so the power is 10⁰
But it is now in Scientific Notation

Check!

After putting the number in Scientific Notation, just check that:

• The "digits" part is between 1 and 10 (it can be 1, but never 10)
• The "power" part shows exactly how many places to move the decimal point

 

Why Use It?

Because it makes it easier when you are dealing with very big or very small numbers, which are common in Scientific and Engineering work.

Example: it is easier to write (and read) 1.3 × 10^-9 than 0.0000000013

It can also make calculations easier, as in this example:

Example: a tiny space inside a computer chip has been measured to be 0.00000256m wide, 0.00000014m long and 0.000275m high.
What is its volume?
Let's first convert the three lengths into scientific notation:

• width: 0.000 002 56m = 2.56×10^-6
• length: 0.000 000 14m = 1.4×10^-7
• height: 0.000 275m = 2.75×10^-4

Then multiply the digits together (ignoring the ×10s):
2.56 × 1.4 × 2.75 = 9.856
Last, multiply the ×10s:
10^-6 × 10^-7 × 10^-4 = 10^-17 (easier than it looks, just add -6, -4 and -7 together)

The result is 9.856×10^-17 m³

It is used a lot in Science:

Example: Suns, Moons and Planets

The Sun has a Mass of 1.988 × 10³⁰ kg.
It would be too hard for scientists to have to write 1,988,000,000,000,000,000,000,000,000,000 kg